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Responsabili:

Federica Galluzzi  ed  Elena Martinengo
 

Nel calendario si indicano i seminari di geometria algebrica e altre attività di interesse, organizzate dall'Università e dal Politecnico di Torino.

Evento

Titolo: An existence result on rational normal curves
Quando: 19/11/2024 - 15:00
Dove: Palazzo Campana - TORINO
Aula: Aula 5
Relatore: Stefano Canino
Afferenza: Politecnico di Torino
Locandina: Locandina

Descrizione:

Abstract: A very classical result, the Castelnuovo Lemma, states that, given d+3 points in general position in P^d, there is a unique rational normal curve of degree d passing through them. An easy argument shows that asking for a rational normal curve to pass through a point, imposes, in the parameter spaces of rational normal curves, the same number of conditions imposed by asking for a rational normal curve to be (d-1)-secant to a codimension 2 projective subspace of P^d. For this reason, it is quite natural to pose the following problem: given p points in P^d and l codimension 2 subspaces in P^d with p+l=d+3, is there a rational normal curve passing through the points and being (d-1)-secant to the l projective subspaces? A paper of Carlini and Catalisano (2007) solves all the cases except for (p,l)=(0,d+3). In this talk we show how to solve this missing case by using symmetric polynomials.

 

Sede

Sede: Palazzo Campana
Indirizzo: Via Carlo Alberto n.10
CAP: 10123
Città: TORINO